Negative sequence network having a frequency compensated filter

ABSTRACT

Disclosed is a phase sequence network. The network is compensated for frequency variations in the signal applied to the sequence network so as to develop a desired sequence component output that is accurate over a limited but adequate range of frequencies.

BACKGROUND

This invention relates to a sequence network or filter used for the protection of an electrical transmission line and generators, and more particularly, to a sequence network having phase shift networks on its input stage which provides compensation for frequency variations of the applied input signal so as to develop a substantially accurate desired sequence component in spite of input frequency variation.

As is known, phase sequence networks are responsive to selected symmetrical components of current in a polyphase alternating current electric power circuit. The theory of symmetrical components is well understood by those skilled in the art of electric power transmission and distribution. In accordance with this theory, the phase currents or voltages in any unbalanced three-phase alternating-current electric circuit can be resolved into three sets of symmetrical, balanced current or voltages vectors known respectively as positive sequence, negative sequence and zero sequence component. The negative and zero sequence components of circuit current and voltage are not present under balanced circuit conditions. A more detailed discussion of the theory of symmetrical components can be found in the textbook, Symmetrical Components, by Wagner and Evans, published by McGraw-Hill in 1933.

It has been known that certain circuits, called sequence networks or filters, can be connected to an electric-power system to provide an output signal that is proportional to the magnitude of the negative sequence components of current. These sequence networks or filters are particularly useful in the protective relaying art as they will sense the presence of negative sequence components of current which flow when the power system becomes unbalanced due to abnormal or fault conditions. It has also been known in the protective relaying art that it is desirable to have a sequence network that senses the positive sequence components of current of the power system. A sequence network commonly utilized in protection of a high voltage transmission line and generators is described in U.S. Pat. No. 4,342,062.

Typically, sequence networks derive their negative or positive sequence components from the voltage or current quantities of a power source having a rated frequency supplying a three phase transmission line. A difficulty with prior sequence networks is that their accuracy may be seriously degraded by changes in the input frequency of the power source. Such frequency changes sometimes occur on electrical power distribution systems where these sequence networks are commonly used. For example, assuming the sequence network desires to sense the negative sequence component related to the three phase transmission line and further assuming only the positive sequence component is applied to the network, for this condition it is desired that no output quantity be developed by the sequence network. However, if the input frequency of the power source changes, an output quantity of the sequence network may occur even though the input signal to the sequence network still contains only a positive sequence component. The output is obviously an error since it indicates a negative sequence component where none exists. This error occurs because the phase and amplitude characteristics of the phase shift networks typically used on one or more phases to obtain phase shifted quantities relative to the other phase or phases vary with deviations from the rated frequency of the power source. Further, this variation may be such that undesired sequence components may no longer be cancelled. It is desired that a sequence network be provided for developing positive or negative components whose performance is substantially constant even though the frequency of the power source supplying the transmission line may be a variable quantity.

One use of a desired sequence network may be in the "art of instrumentation". The term "art of instrumentation" is meant to represent the art of developing in a very accurate manner a function which may be monitored and measured, and which function is an indication of a particular condition of an overall system. For example, in the field of power generation the unbalanced currents, indicative of a power loss quantity, developed within the power generator may be manifested by the presence of negative sequence current. If this negative sequence current is accurately sensed by a sequence network the output of the sequence network may be routed to an external instrumentation circuit, which, in turn may develop an accurate quantity indicative of a primary characteristic, that is the power loss quantity, of the power generator.

Accordingly, one object of the present invention is to provide a sequence network for accurately developing positive or negative sequence components over a limited but adequate range of frequency variations.

It is another object to accurately develop the positive or negative sequence components so that they may be further used for instrumentation purposes.

These and other objects of the present invention will become apparent to those skilled in the art upon consideration of the following description of the invention.

Summary of the Invention

This invention is directed to a sequence network. The sequence network is adapted to be coupled to each phase of a three-phase transmission line by coupling means which develops three signals A, B, and C respectively representative in magnitude and phase of the transmission line currents or of the transmission line voltages. The sequence network is adapted to detect one phase sequence component and reject another phase sequence component of the transmission line currents or voltages. The sequence network has an operative frequency equal to the rated frequency of the transmission line and comprises:

(a) a first phase shift network having applied thereto the signal A and developing a first output signal. The first phase shift network comprises two legs each contributing substantially equal phase shifts but each leg contributing opposite variation in phase shift in response to frequency changes such that the total phase shift of the first phase shift network does not vary substantially in response to frequency changes within a predetermined limited range encompassing the operating frequency;

(b) a second phase shift network having applied thereto said signal B and developing a second output signal. The second phase shift network provides a phase shift opposite to that provided for signal A. The second phase shift network comprises two legs each contributing substantially equal phase shifts but each leg contributing opposite phase shift variations in response to frequency changes such that the total phase shift of the second phase shift network does not vary substantially in response to frequency changes within the predetermined limited range;

(c) first means for summing the first and second output signals so as to obtain a resultant signal that is representative of the vector sum of the first and second output signals;

(d) an additional network with no substantial phase shift properties having applied thereto the signal C for developing a third output signal in phase with signal C and having a magnitude equal to the resultant signal for the particular phase sequence component to be rejected, and;

(e) means for summing the third output signal with the resultant signal and developing a fourth output signal representative of the particular phase sequence component to be detected.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a circuit arrangement of one embodiment of the present invention.

FIGS. 2a, 2b, 3a and 3b show the characteristics of the first network of FIG. 1.

FIGS. 4a, 4b show the characteristics of the second network of FIG. 1.

FIG. 5 shows an equivalent circuit of one of the legs of FIG. 4a.

FIGS. 6a and 6b show respectively a vector representation related respectively to positive and negative sequence inputs to the circuit of FIG. 1 or FIG. 7.

FIG. 7 shows a circuit arrangement of another embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 shows a portion of a three phase transmission line 12 interconnected to a three-phase Generator acting as a power source. FIG. 1 further shows the secondary windings of current transformers 14_(a), 14_(b) and 14_(c) coupled respectively to phases A, B, and C of the transmission line 12. The secondary windings 14_(a), 14_(b) and 14_(c) are arranged in a delta-connected manner. One side of each of the secondary windings 14_(a), 14_(b) and 14_(c) are respectively coupled to wye connected load resistors R_(a), R_(b) and R_(c). The windings 14_(a), 14_(b) and 14_(c) respectively couple the current quantities I_(a), I_(b) and I_(c) to R_(a), R_(b) and R_(c), across which I develops the V_(a), V_(b), and V_(c) voltages applied to a circuit 10 of FIG. 1. For the arrangement shown in FIG. 1, the delta connection of transformers 14_(a), 14_(b) and 14_(c) eliminates the zero-sequence currents that may otherwise flow into the circuit 10 of FIG. 1, and the wye connected load resistors R_(a), R_(b) and R_(c) provide a path for current from the secondary windings 14_(a), 14_(b), and 14_(c) to a neutral 16 of the circuit 10 of FIG. 1.

In general, the circuit 10 of FIG. 1 for one embodiment of the present invention is a sequence network in which the degradation of accuracy, discussed in the Background, created by frequency variations in the power source, such as the generator of FIG. 1, is substantially reduced. This reduction is primarily achieved by the phase shift networks 20 and 22 of the circuit 10. As will be described, the networks 20 and 22 exhibit substantially reduced phase variations typically created by frequency changes. The circuit illustrated in FIG. 1 detects positive sequence components if the normal phase sequence a, b, c is assumed. As will be discussed hereinafter, interchanging the signals to any two inputs results in detection of negative sequence components.

As will be further discussed, the sequence network 10 is adapted to detect one phase sequence component and reject another sequence component of the transmission line currents or voltages. The sequence network 10 has an operating frequency equal to the rated frequency of the transmission line. The first network 20 of the sequence network 10 comprising two legs each contributing substantially equal phase shifts but each leg contributing opposite variation in phase shift in response to frequency changes such that the total phase shift of the first phase shift network does not vary substantially in response to frequency changes within a predetermined limited range encompassing the operating frequency. The second network 22 provides a phase shift opposite to that provided by network 20. The second phase shift network 22 comprises two legs each contributing substantially equal phase shifts but each leg contributing opposite phase shift variations in response to frequency changes such that the total phase shift of the second phase shift network does not vary substantially in response to frequency changes within the predetermined limited range encompassing the operating frequency. The first and second networks 20 and 22 are summed so as to obtain a resultant signal that is representative of the vector sum of the first and second output signals.

An additional network, that is network 24, is provided with no substantial phase shift properties. The network 24 develops a third output signal having a magnitude equal to the resultant signal for the particular phase sequence component to be rejected.

FIG. 1 shows the sequence network circuit 10 having an operational amplifier OP AMP 30. The OP AMP 30 has an inverting and non-inverting input. The OP AMP 30 has an output coupled back to its inverting input by a feedback resistor R_(FB) having a value selected so as to determine the gain of the OP AMP 30. The non-inverting input of OP AMP 30 is coupled to the neutral 16. The inverting input of the OP AMP 30 is coupled to input networks 20, 22, and 24.

The first input network 20 develops a first output signal and is comprised of, a first resistor R₁, and a first and second capacitor C₁ and C₂. The resistor R₁ has one of its ends connected to one side of capacitor C₂ and also to the inverting input of the OP AMP 30 via a summing junction 26. The other side of resistor R₁ is connected to one end of the capacitor C₁. The other end of capacitor C₁ is connected to the other end of capacitor C₂ and is also adapted to receive the quantity V_(a).

The second input network 22 develops a second output signal and is comprised of, second and third resistors R₂ and R₃, a third capacitor C₃ and a first inductor L₁. The resistor R₂ has one end connected to one end of inductor L₁ and is also adapted to receive the quantity V_(b). The resistor R₃ has one end connected to the other end of resistor R₂ and also to one end of capacitor C₃. The other end of resistor R₃ is connected to the other end of inductor L₁ and to the inverting input of the OP AMP 30 via the summing junction 26. The other end of the capacitor C₃ is connected to the non-inverting input of the OP AMP 30.

The third input network 24 develops a third output signal and is comprised of a fourth resistor R₄ having one of its ends adapted to receive the quantity V_(c), and its other end connected to the inverting input of the OP AMP 30 via the summing junction 26.

As is to be discussed hereinafter, summing junction 26 provides the means for summing the first and second output signals into a resulting signal. Summing junction 26 further provides the means for summing the resultant signal with the third output signal.

In one embodiment of this invention, the OP AMP 30 in response to the receipt of signals filtered by networks 20, 22 and 24 develops a V_(OUT) signal whose magnitude is proportional to the negative sequence component of the three phase currents I_(a), I_(b) and I_(c). The signal V_(OUT) is accurately developed by the circuit 10 over a limited but adequate range of frequencies. In order that the obtainment of the desired signal V_(OUT) may be more fully described, reference is now made to a detailed description of each of the networks 20, 22, and 24.

The network 20 is a phase lead type network. Characteristics of network 20 are shown in FIG. 2a and 2b. FIG. 2b shows the real summing junction current component of network 20 along the X axis and the imaginary (j) reactive current component of network 20 along the Y axis. FIG. 2a is a diagram illustrating currents I₁, I₂ and I₃ flowing within the network 20. A vector illustration of the I₁, I₂ and I₃ currents of FIG. 2a is shown in FIG. 2b. FIG. 2b shows angles α₁, α₂, and α₃ respectively associated with quantities I₁, I₂ and I₃. FIG. 2b shows the two current components, I₁ and I₂ combined to form I₃. As is well known, both the amplitude and phase of the quantities I₁, I₂ and I₃ may vary with frequency.

The locus, that is the path of the curve, of I₁ of FIG. 2b is shown as the semicircle 34. The vector length of I₁ moves clockwise with increasing frequency. The locus of I₂ is the vertical axis of FIG. 2b with the vector length of I₂ increasing with frequency. The quantities I₁ and I₂ are shown in FIG. 2b combined to form I₃ (refer to the right hand side of FIG. 2b). When the frequency increases, I₁ moves clockwise around semicircle 34 decreasing the angle α₁ in its movement. During these frequency increases I₂ remains vertical and also increases in magnitude with frequency increases so that the angle α₂ increases during the decreasing angle α₁. The result is that this network's summing current I₃ and its angle α₃ remain reasonably constant with frequency variations such as those of ±5 percent of the rated frequency.

A desired substantially reduced variation of I₃ is obtained when α₁ and α₂ are selected to approximately equal to each other at the rated frequency of the power source. To select or calculate the component values in my improved network 10, 20 related to α₁ and α₂ and also the other component of my circuit, it is necessary to assume certain conditions. First assume that a three phase signal having the sequence component desired to be rejected is present at all the three inputs to network 10. Under ideal conditions the voltages at each input are equal in magnitude and separated by angles of 120°. These voltages are shown as V_(a), V_(b) and V_(c) of both FIGS. 6a and 6b to be discussed hereinafter. The currents through R_(a), R_(b), and R_(c) are obtained from the current transformer input currents I_(a), I_(b), and I_(c) respectively, by the previously discussed wye to delta transformations of transformer 14. The component calculations of my circuit 10 may proceed by assuming |V_(ph) |=|V_(a) |=|V_(b) |=|V_(c) |. These voltages are phase to neutral voltages and cause the development of equal magnitude currents I₃ and I₆ at the summing junction 26 in response to V_(a) and V_(b) inputs respectively.

In one embodiment of the present invention, it is desired that the α₃ quantity of the I₃ current of network 20 be of a value of +15°. Still further for this embodiment it is desired that the α₁ and α₂ quantities of I₁ and I₃, respectively, be of a value of +7.5°. Reference is now made to FIG. 3 so as to further describe the desired calculations related to the quantities α₁, α₂ and α₃ all of network 20.

FIG. 3 is a simplified version of FIG. 2. FIG. 3 is composed of FIGS. 3a and 3b. FIG. 3b shows the I₃ quantity as having an angle α₃ with a typical value of +15°. FIG. 3b further shows I₃ as being the vector sum of the quantities I₁ and I₂. The quantity I₂ contributing to the magnitude of I₃ is shown by use of a solid line. The reactive component of I₁ contributing to the magnitude of I₃, which is approximately equal to I₂, is shown in phantom.

The quantities I₂ and I₃ of FIG. 3b and also FIG. 2b may be shown by expressions 1 and 2:

    2I.sub.2 =I.sub.3 sin 15°                           (1)

    I.sub.2 =(I.sub.3 /2) sin 15°                       (2)

The reactance X_(C2) of C₂ of network 20 of FIG. 3a may be shown by expression 3: ##EQU1##

Once X_(C2) is calculated, the value of C₂ may be obtained by solving expression 4: ##EQU2## where ω=2πf, and f is the operating frequency of the network 20.

The magnitude of I₁ of FIG. 3b may be determined by expression 5: ##EQU3##

The impedance Z₁ of the path of the current I₁ of FIG. 3a may be determined by expression 6: ##EQU4##

The values of R₁ and X_(C1) may be trigonometrically expressed in terms of Z₁ as R₁ =Z₁ cos 7.5° and X_(C1) =Z₁ sin 7.5° respectively. When X_(C1) is determined, the value of C₁ may be calculated in a similar manner as C₃ of expression (4).

It should now be appreciated that the practice of this invention described for network 20 provides a first and a second leg each contributing an equal phase shift to I₃ but having opposite shift changes versus frequency so as to develop an output signal from network 20 that is substantially constant in spite of frequency variations. The first leg of network 20 is comprised of a serially arranged resistor R₁ and capacitor C₁. The second leg of network 20, which is in parallel with the first leg, is comprised of a capacitor C₂. The equal phase angles desired for one embodiment having α₃ =+15°, α₁ =+7.5°, and α₂ =+7.5°, are selectable in accordance with the hereinbefore given description.

Reference is now made to FIGS. 4a and 4b so as to describe the desired calculations for the network 22 having a lag-type characteristic. In accordance with the previously mentioned first embodiment of the present invention, it is further desired that the α₃ =+15° desired for network 20 be considered in determining the selection of the desired phase shift of network 22.

FIG. 4a shows the currents I₄ and I₅ flowing within the legs of network 22 and which combine to form the current I₆ at summing junction 26. FIG. 4a further shows the quantity V_(b) at the input of lag network 22.

FIG. 4b shows the relationship of the currents I₄, I₅ and I₆ of network 22 of FIG. 4a. FIG. 4b further shows the current I₅ of FIG. 4d as a reactive negative going vector and the current I₄, shown in phantom, as a lagging vector. FIG. 4_(b) further shows a vertical arrow for I₄ in phantom for the reactive component of I₄. This reactive component of I₄ is approximately equal to I₅, and contributes to the magnitude of I₆. FIG. 4b still further shows the I₆ current as having a negative angle α₆ =15° and being displaced from V_(b) in a negative direction.

The currents I₅ and I₆ of FIG. 4b may be expressed by relationships 7 and 8;

    2I.sub.5 =I.sub.6 sin 15°                           (7)

    I.sub.5 =I.sub.6 /2 sin 15°                         (8)

The impedance X_(L1) of the L₁ leg, of FIG. 4a, may be described by relationship 9: ##EQU5##

When X_(L1) is determined, the value of L₁ may be obtained from expression 10: ##EQU6## where ω=2πf

For the network 22 of FIG. 4a of the values or R2, R3, and C3 also have to be calculated. For the calculations, to be described, it is assumed that R₂ =R₃. In one embodiment of the present invention, it is desired that the voltage across C₃ have a desired -7.5° C. phase angle. Further, a certain relationship between X_(C3) and R₂ is desired and this relationship may best be described with reference to FIG. 5.

FIG. 5 is an equivalent circuit of one of the legs of network 22 comprised of the resistors R2 and R3, shown in FIG. 5 as R₂ /2, and the capacitor C₃. FIG. 5 shows the voltage of C₃ between summing junction 26 and neutral 16 as V_(C3). Still further, the equivalent circuit of FIG. 5 is shown to have applied to it the quantity V_(b).

The V_(C3) shown in FIG. 5 may be expressed by relationship 12: ##EQU7##

As mentioned, for one embodiment it is desired that the quantity V_(C3) have a phase angle of -7.5° and as such the denominator of expression (12) may be determined by expression 13: ##EQU8##

From expression (13) the determination of C₃ may be shown by expression 14: ##EQU9##

From the expressions 12 and 14 the V_(C3) may be expressed by relationship 15: ##EQU10##

Expression 15 may be simplified by cancelling the ωR₂ terms of its denominator so as to yield expression 16: ##EQU11##

Still further, expression 16 may be further simplified and shown as such by expression 17: ##EQU12##

In accordance with the one embodiment of this invention, it is desired that the I₄ current shown in FIGS. 4a and 4b of network 22 have a value expressed by relationship 18: ##EQU13##

Since the quantity I₄ of expression 18 has the relationship I₄ =(V_(C3) /R₃); then the value of R₃ may be shown by expression 19: ##EQU14##

Similarly, since the quantity of I₅ of expression 19 has the relationship ##EQU15## then R₃ may be shown by expression 20: ##EQU16##

From expression 17 it has been determined that V_(C3) =0.49572 V_(b) so R₃ may be expressed by relationship 21: ##EQU17##

As previously mentioned, R₂ and R₃ have been assumed to be of an equal value so that R₂ may also be determined by that of expression (21).

It should now be appreciated that the practice of this invention provides a network 22 for developing a desired current I₆ having a desired lagging phase angle α₆ of -15° so as to correspond to the desired network 20 having the desired leading phase angle α₃ =+15°.

For a sequence network like the first embodiment of the present invention which develops a positive sequence component output it is desired that quantities |I₃ | and |I₆ | be equal, and the phase angle between I₃ and I₆ be 90° such as shown in FIG. 6a. FIG. 6a still further shows the quantities V_(a), V_(b), and V_(c) having their desired 120° interrelated phase displacements. Further still, FIG. 6a shows the desired orientation of negative sequence type inputs to the circuit 10. Still further, as illustrated in FIG. 6a, to develop the desired positive sequence component of the first embodiment it is desired that the quantities |I₃ | and |I₆ | be vectorially combined so as to develop a resultant quantity I_(R) =1.414 |I₃ |. The resultant quatity I_(R) may also be selected to be equal to 1.414|I₆ | (not shown). The I_(R) quantity has a phase angle of 180° with respect to I₇, and I₇ is the current from the third input when the input is of a negative sequence type.

The current I₇, also shown in FIG. 6a, contributes to the development of resultant quantity I_(R) in its reaction with the currents I₃ and I₆ of the first network present at summing junction 26. In order that I₇ contribute to the desired resultant quantity |I_(R) |=1.414 I₃, the resistor value of R₄ of the third network 24 may be selected in accordance with expression 22; ##EQU18##

In the operation of the circuit arrangement 10 of FIG. 1 having the applied signals of FIG. 6a, the signal V_(a) is shifted forward in phase 15° so as to develop I₃ of the first network 20 and V_(b) is shifted back by 15° so as to develop I₆ of the second network 22. The angle between I₃ and I₆ is now 90°. I₃ and I₆ are summed so that resultant I_(R) is out of phase with V_(b) and has an amplitude 1.414 times that of I₃ or I₆. The current I₇ has no substantial phase shift with respect to V_(c). The magnitude of I₇ is adjusted by the selection of R₄ so as to match or equal that of I_(R). The summing of I_(R) and I₇ gives a zero output signal in response to the negative sequence type signals V_(a), V_(b) and V_(c) shown in FIG. 6a. More particularly for one embodiment of the present invention, if the signals V_(a), V_(b), and V_(c), representative of negative sequence type signals to be rejected by the circuit 10, are applied to circuit 10 then the output V_(OUT) is substantially zero.

Typically, the input signals V_(a), V_(b), and V_(c) contain both positive and negative sequence components. Input signals V_(a) V_(b), and V_(c) of a positive sequence type are shown in FIG. 6b. The positive sequence type signals of V_(a), V_(b) and V_(c) develop currents I₃ shifted forward by 15° from V_(a), I₆ shifted back by 15° from V_(b), and I₇ with no substantial phase shift with respect to V_(c). The currents I₃, I₆ and I₇ at summing junction 26 do not cancel. In response to the positive sequence type signals the sequence network 10 of FIG. 1, develops an output signal V_(OUT) representative of the combined vector type currents I₃, I₆ and I₇ of FIG. 6b. The magnitude of V_(OUT) being representative of the positive sequence component of the currents I_(a), I_(b), and I_(c) flowing in the transmission line 12 and also representative of the applied voltages V_(a), V_(b), and V_(c).

It should now be appreciated that the circuit 10 of FIG. 1 selects a positive sequence component with an accuracy that is substantially constant in spite of frequency variations in its applied signals V_(a), V_(b), and V_(c). The accurate and constant output signal V_(OUT) of FIG. 1 is developed by my networks 20, 22 and 24 in accordance with the practice of my invention.

Still further, although the circuit 10 of FIG. 1 has been described with regard to obtaining the positive sequence component of transmission line 12, the negative sequence quantity may be easily obtained by the practice of this invention by rearranging the inputs to circuit 10 so as to simply switch any two of the three inputs. For example, if the input V_(b) and V_(c) shown as applied to FIG. 1 are switched then the signals V_(a), V_(c), and V_(b) have relative phase position representation of a negative sequence orientation and the circuit 10 of FIG. 1, in turn, develops an output signal V_(OUT) representative of the negative sequence component of the current I_(a), I_(b) and I_(c) flowing in transmission line 12.

The hereinbefore given description is related to circuit 10 of FIG. 1. In practice, the calculation of component values of circuit 10 and the arrangement of electronic components may be improved so as to permit a trimming or tuning of the desired values by the circuit 40 of FIG. 7.

FIG. 7 shows the circuit 40 as having the previously described networks 20, 22, and 24, the OP AM 30, and R_(FB) all of FIG. 1. The description of the circuit components of FIG. 1, shown in FIG. 7, is also applicable to circuit 40 of FIG. 7 Although the front end coupling of circuit 10 to transmission line 12, via current transformers 14a, 14b and 14c and resistors R_(a), R_(b) and R_(c) is not shown in FIG. 7, it is applicable to the second embodiment of the present invention circuit 40 of FIG. 7.

FIG. 7 shows a serial arrangement (not shown in FIG. 1) between V_(a) and V_(b) voltages applied to circuit 40, comprised of resistor R₆, potentiometer R₇ having one end of its adjustable arm coupled to neutral 16, and a resistor R₈. FIG. 7 further shows a potentiometer R₅ (not shown in FIG. 1) serially arranged with resistor R₄. The resistors R₄ and R₅ comprise network 24.

FIG. 7 has two adjustment potentiometers R₅ and R₇ that permit the circuit 40 to be adjusted to compensate for component inaccuracies. In practice, these potentiometers R₅ and R₇ are adjusted by applying pure negative sequence signals for I_(A), I_(B), and I_(C) represented by the signals V_(a), V_(b), V_(c), I₃, I₆ and I₇ of FIG. 6a and nulling the output V_(OUT) using potentiometers R₅ and R₇.

The circuit 40 of FIG. 7 and the circuit 10 which detect the positive sequence component may also operate to detect the other sequence component by simply reversing any two input signals in a manner as described for circuit 10 of FIG. 1. For example, if it is desired that a signal V_(OUT) be representative of the negative sequence component of the currents I_(a), I_(b), and I_(c) flowing in transmission line 12, then currents I_(a) and I_(b) routed to circuit 40 via signal V_(a) and V_(b) are simply interchanged.

The circuit 40 of FIG. 7 and also the circuit 10 of FIG. 1 each operate in a desired manner so as to provide typical results shown in Table 1.

                  TABLE 1                                                          ______________________________________                                         Frequency                                                                      (in Hz)     Error Value (in percent)                                           ______________________________________                                         57          0.38                                                               58          0.25                                                               59          0.14                                                               60          0.11                                                               61          0.19                                                               62          0.29                                                               63          0.39                                                               ______________________________________                                    

Table 1 shows two columns: (1) the frequency variations related to the quantities I_(a), I_(b) and I_(c) and V_(a), V_(b), and V_(c) applied to the circuits 40 and 10 of the present invention, and (2) the typical error values given in percentages. The error values are applicable to the development of an output signal V_(OUT) for both positive and negative sequence components. For example, a percentage error of 0.11 for 60 Hz application may be developed for the negative sequence component in response to quantities I_(a), I_(b) and I_(c) which do not have any negative sequence components.

The resistive, capacitive, and inductive components of circuit arrangement 10 for a 60 Hz application may have typical values as given in Table 2.

                  TABLE 2                                                          ______________________________________                                         Components         Typical Value                                               ______________________________________                                         R.sub.1            9914 ohms                                                   R.sub.2            5088 ohms                                                   R.sub.3            5088 ohms                                                   R.sub.4            7070 ohms                                                   C.sub.1            1.979 m farads                                              C.sub.2            0.03445 m farads                                            C.sub.3            0.1372 m farads                                             L.sub.1            204 henry                                                   ______________________________________                                    

It should now be appreciated that the present invention provides a sequence network for accurately developing positive or negative sequence components over a limited but adequate range of frequency variations.

While I have shown and described particular embodiments of my invention, it will be obvious to those skilled in the art that various changes and modifications may be made without departing from my invention in its broader aspects; and I, therefore, intend herein to cover all such changes and modifications as fall within the true spirit and scope of my invention. 

What I claim is:
 1. A sequence network adapted to be coupled to each phase of a three phase transmission line by coupling means which develops three signals A, B, and C respectively representative in magnitude and phase of the transmission line currents or of the transmission line voltages, said sequence network being adapted to detect one phase sequence component and reject another phase sequence component of the transmission line currents or voltages, said sequence network having an operating frequency equal to the rated frequency of the transmission line and comprising:(a) a first phase shift network having applied thereto said signal A and developing a first output signal, said first phase shift network comprising two legs each contributing substantially equal phase shifts but each leg contributing opposite variation in phase shift in response to frequency changes such that the total phase shift of the first phase shift network does not vary substantially in response to frequency changes within a predetermined limited range encompassing said operating frequency, (b) a second phase shift network having applied thereto said signal B and developing a second output signal, said second phase shift network providing a phase shift opposite to that provided for signal A, said second phase shift network comprising two legs each contributing substantially equal phase shifts but each leg contributing opposite phase shift variations in response to frequency changes such that the total phase shift of the second phase shift network does not vary substantially in response to frequency changes within said predetermined limited range, (c) first means for summing said first and second output signals so as to obtain a resultant signal that is representative of the vector sum of said first and second output signals, (d) an additional network with no substantial phase shift properties having applied thereto said signal C for developing a third output signal in phase with signal C and having a magnitude equal to said resultant signal for the particular phase sequence component to be rejected, and (e) means for summing said third output signal with said resultant signal and developing a fourth output signal representative of the particular phase sequence component to be detected.
 2. The sequence network according to claim 1, wherein said sequence network comprises:(a) an operational amplifier having an output, a non-inverting input coupled to a neutral associated with signals A, B, and C and an inverting input coupled to the output of the operational amplifier by a resistor R_(FB) ; (b) said first network for developing the first output signal and comprising a first resistor R₁, and a first and second capacitor C₁ and C₂, said resistor R₁ has one of its ends connected to one side of capacitor C₂ and to said inverting input, the other side of resistor R₁ is connected to one end of the capacitor C₁ the other end of capacitor C₁ being connected to the other end of capacitor C₂ and is adapted to receive the signal A, said resistor R₁ and capacitor C₁ forming a first leg of the first network and the capacitor C₂ forming a second leg of the first network; (c) said second network for developing the second output signal and comprising second and third resistors R₂ and R₃, a third capacitor C₃ and a first inductor L₁, said resistor R₂ has one end connected to one end of inductor L₁ and is adapted to receive the signal B, said resistor R₃ has one end connected to the other end of resistor R₂ and one end of capacitor C₃, the other end of resistor R₃ is connected to the other end of inductor L₁ and to the inverting input, said inductor L₁ forms a first leg of the second network, said resistors R₂ and R₃, and the capacitor C₃ forming a second leg of the second network, the other end of the capacitor C₃ being connected to the non-inverting input which is also coupled to the neutral related to the input quantities; said inverting input of said operational amplifier providing a junction for summing the first and second output signal so as to develop the resultant signal; (d) said additional network developing the third output signal and comprised of a fourth resistor R₄ having one of its ends adapted to receive the signal C and its other end connected to the inverting input, wherein;the component values of said first network being selected so as to provide said desired phase shifts thereof; the component values of said second network being selected so as to provide said desired phase shifts thereof; and the value of R₄ being selected so as to provide said third output signal.
 3. The sequence network according to claim 1, wherein said negative sequence network comprises:(a) an operational amplifier having an output, a non-inverting input coupled to a neutral associated with signals A, B, and C and an inverting input coupled to the output of the operational amplifier by the resistor R_(FB) ; (b) said first network for developing the first output signal and comprising a first resistor R₁, a sixth resistor R₆, a first variable portion of a seventh variable resistor R₇ and a first and second capacitors C₁ and C₂, said resistor R₇ having two ends and a variable arm having one of its ends coupled to said neutral, said first variable portion of resistor R₇ being coupled to one end of said resistor R₆, said resistor R₁ has one of its ends connected to one side of capacitor C₂ and to said inverting input, the other side of resistor R₁ is connected to one end of the capacitor C₁, the other end of capacitor C₁ being connected to the other end of capacitor C₂ by said sixth resistor, and said other end of said resistor R₆ being adapted to receive said signal A, said resistor R₁ and capacitor C₁ forming a first leg of the first network and the capacitor C₂ forming a second leg of the first network; (c) a second input network comprising a second and third resistors R₂ and R₃, a second variable portion of said seventh variable resistor R₇, an eighth resistor R₈, a third capacitor C₃, and a first inductor L₁, said second variable portion of resistor R₇ being coupled to one end of resistor R₈, said resistor R₂ having one end connected to one end of inductor L₁ by said resistor R₈ and said other end of said resistor R₈ being adapted to receive said signal B, said resistor R₃ has one end connected to the other end of resistor R₂ and one end of capacitor C₃, the other end of resistor R₃ being connected to the other end of inductor L₁ and to the inverting input, said inductor L₁ forming the first leg of the second network, said resistors R₂ and R₃, and the capacitor C₃ forming the second leg of the second network, the other end of the capacitor C₃ being connected to the non-inverting input, (d) a third input network for developing said third output signal and comprised of a fourth resistor R₄ and a variable resistor R₅, said fourth resistor R₄ having one of its ends adapted to receive said signal C and its other end connected to the inverting input by said fifth variable resistor, wherein;the component values of said first network being selected so as to provide said desired phase shifts thereof; the component values of said second network being selected so as to provide said desired phase shifts thereof; the component values of said third network being selected so as to provide said third output signal; and said variable resistors R₅ and R₇ being adjusted so as to develop a zero voltage output for the fourth output signal in response to phase sequence components of the signal A, B and C selected to be rejected.
 4. The sequence network according to either claim 1, claim 2 or claim 3, wherein said component values of said first network is selected so as to provide (1) the total shift value of a positive fifteen (15) degrees comprised of a positive seven and one-half (7.5) degrees phase shift contributed by each of said first and second legs of the first network, and component values of said second network is selected so as to provide (2) a total phase shift of value of a negative fifteen (15) degrees comprised of a negative seven and one-half (7.5) contribution by each of said first and second legs of said second network, said component values being selected in accordance with said operating frequency of said sequence network. 